Hi Cristoforo, you getting the point right. If, for example, only three "object sums" are possible (0, 1 and 2).

$nElements = 1:
Sum = 0 -> 0
Sum = 1 -> 1
Sum = 2 -> 2

$nElements = 2:
Sum = 0 -> 0+0
Sum = 1 -> 0+1 1+0
Sum = 2 -> 0+2 1+1 2+0
Sum = 3 -> 1+2 2+1
Sum = 4 -> 2+2

$nElements = 3:
Sum = 0 -> 0+0+0
Sum = 1 -> 0+0+1 0+1+0 1+0+0
Sum = 2 -> 0+0+2 0+1+1 0+2+0 1+0+1 1+1+0 2+0+0
Sum = 3 -> 0+1+2 0+2+1 1+0+2 1+1+1 1+2+0 2+0+1 2+1+0
Sum = 4 -> 0+2+2 1+1+2 1+2+1 2+0+2 2+1+1 2+2+0
Sum = 5 -> 1+2+2 2+1+2 2+2+1
Sum = 6 -> 2+2+2

And so on...
[download]

Of course, there is some redundancy in there, for ex. Element = 3, sum = 1 could be treated as (3*((p0)**2)*p1). But, how to generate this automatically and fast ?

Thanks, FFRANK